33 research outputs found
Anti-deSitter universe dynamics in LQC
A model for a flat isotropic universe with a negative cosmological constant
and a massless scalar field as sole matter content is studied within
the framework of Loop Quantum Cosmology. By application of the methods
introduced for the model with , the physical Hilbert space and the
set of Dirac observables are constructed. As in that case, the scalar field
plays here the role of an emergent time. The properties of the system are found
to be similar to those of the FRW model: for small energy densities, the
quantum dynamics reproduces the classical one, whereas, due to modifications at
near-Planckian densities, the big bang and big crunch singularities are
replaced by a quantum bounce connecting deterministically the large
semiclassical epochs. Thus in Loop Quantum Cosmology the evolution is
qualitatively cyclic.Comment: Revtex4, 29 pages, 20 figures, typos correcte
Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
Analytical and numerical methods are developed to analyze the quantum nature
of the big bang in the setting of loop quantum cosmology. They enable one to
explore the effects of quantum geometry both on the gravitational and matter
sectors and significantly extend the known results on the resolution of the big
bang singularity. Specifically, the following results are established for the
homogeneous isotropic model with a massless scalar field: i) the scalar field
is shown to serve as an internal clock, thereby providing a detailed
realization of the `emergent time' idea; ii) the physical Hilbert space, Dirac
observables and semi-classical states are constructed rigorously; iii) the
Hamiltonian constraint is solved numerically to show that the big bang is
replaced by a big bounce. Thanks to the non-perturbative, background
independent methods, unlike in other approaches the quantum evolution is
deterministic across the deep Planck regime. Our constructions also provide a
conceptual framework and technical tools which can be used in more general
models. In this sense, they provide foundations for analyzing physical issues
associated with the Planck regime of loop quantum cosmology as a whole.Comment: Revised version to appear in Physical Review D. References added and
typos correcte
Loop quantum cosmology of k=1 FRW models
The closed, k=1, FRW cosmology coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the k=0 case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semi-classical at some late time, the big-bang is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the `difficulties' pointed out by Green and Unruh in the k=1 case do not arise in a more systematic treatment. As in k=0 models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the k=0 case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna's recent work addressed to computational physicists
Quasi-local rotating black holes in higher dimension: geometry
With a help of a generalized Raychaudhuri equation non-expanding null
surfaces are studied in arbitrarily dimensional case. The definition and basic
properties of non-expanding and isolated horizons known in the literature in
the 4 and 3 dimensional cases are generalized. A local description of horizon's
geometry is provided. The Zeroth Law of black hole thermodynamics is derived.
The constraints have a similar structure to that of the 4 dimensional spacetime
case. The geometry of a vacuum isolated horizon is determined by the induced
metric and the rotation 1-form potential, local generalizations of the area and
the angular momentum typically used in the stationary black hole solutions
case.Comment: 32 pages, RevTex
Multipole Moments of Isolated Horizons
To every axi-symmetric isolated horizon we associate two sets of numbers,
and with , representing its mass and angular
momentum multipoles. They provide a diffeomorphism invariant characterization
of the horizon geometry. Physically, they can be thought of as the `source
multipoles' of black holes in equilibrium. These structures have a variety of
potential applications ranging from equations of motion of black holes and
numerical relativity to quantum gravity.Comment: 25 pages, 1 figure. Minor typos corrected, reference adde
Black hole boundaries
Classical black holes and event horizons are highly non-local objects,
defined in relation to the causal past of future null infinity. Alternative,
quasilocal characterizations of black holes are often used in mathematical,
quantum, and numerical relativity. These include apparent, killing, trapping,
isolated, dynamical, and slowly evolving horizons. All of these are closely
associated with two-surfaces of zero outward null expansion. This paper reviews
the traditional definition of black holes and provides an overview of some of
the more recent work on alternative horizons.Comment: 27 pages, 8 figures, invited Einstein Centennial Review Article for
CJP, final version to appear in journal - glossary of terms added, typos
correcte
Trapped and marginally trapped surfaces in Weyl-distorted Schwarzschild solutions
To better understand the allowed range of black hole geometries, we study
Weyl-distorted Schwarzschild solutions. They always contain trapped surfaces, a
singularity and an isolated horizon and so should be understood to be
(geometric) black holes. However we show that for large distortions the
isolated horizon is neither a future outer trapping horizon (FOTH) nor even a
marginally trapped surface: slices of the horizon cannot be infinitesimally
deformed into (outer) trapped surfaces. We consider the implications of this
result for popular quasilocal definitions of black holes.Comment: The results are unchanged but this version supersedes that published
in CQG. The major change is a rewriting of Section 3.1 to improve clarity and
correct an error in the general expression for V(r,\theta). Several minor
errors are also fixed - most significantly an incorrect statement made in the
introduction about the extent of the outer prison in Vaidya. 17 pages, 2
figure
Quantum geometry and the Schwarzschild singularity
In homogeneous cosmologies, quantum geometry effects lead to a resolution of
the classical singularity without having to invoke special boundary conditions
at the singularity or introduce ad-hoc elements such as unphysical matter. The
same effects are shown to lead to a resolution of the Schwarzschild
singularity. The resulting quantum extension of space-time is likely to have
significant implications to the black hole evaporation process. Similarities
and differences with the situation in quantum geometrodynamics are pointed out.Comment: 31 pages, 1 figur
Phase-space and Black Hole Entropy of Higher Genus Horizons in Loop Quantum Gravity
In the context of loop quantum gravity, we construct the phase-space of
isolated horizons with genus greater than 0. Within the loop quantum gravity
framework, these horizons are described by genus g surfaces with N punctures
and the dimension of the corresponding phase-space is calculated including the
genus cycles as degrees of freedom. From this, the black hole entropy can be
calculated by counting the microstates which correspond to a black hole of
fixed area. We find that the leading term agrees with the A/4 law and that the
sub-leading contribution is modified by the genus cycles.Comment: 22 pages, 9 figures. References updated. Minor changes to match
version to appear in Class. Quant. Gra
Supersymmetric isolated horizons
We construct a covariant phase space for rotating weakly isolated horizons in
Einstein-Maxwell-Chern-Simons theory in all (odd) dimensions. In
particular, we show that horizons on the corresponding phase space satisfy the
zeroth and first laws of black-hole mechanics. We show that the existence of a
Killing spinor on an isolated horizon in four dimensions (when the Chern-Simons
term is dropped) and in five dimensions requires that the induced (normal)
connection on the horizon has to vanish, and this in turn implies that the
surface gravity and rotation one-form are zero. This means that the
gravitational component of the horizon angular momentum is zero, while the
electromagnetic component (which is attributed to the bulk radiation field) is
unconstrained. It follows that an isolated horizon is supersymmetric only if it
is extremal and nonrotating. A remarkable property of these horizons is that
the Killing spinor only has to exist on the horizon itself. It does not have to
exist off the horizon. In addition, we find that the limit when the surface
gravity of the horizon goes to zero provides a topological constraint.
Specifically, the integral of the scalar curvature of the cross sections of the
horizon has to be positive when the dominant energy condition is satisfied and
the cosmological constant is zero or positive, and in particular
rules out the torus topology for supersymmetric isolated horizons (unless
) if and only if the stress-energy tensor is of the form
such that for any two null vectors and with
normalization on the horizon.Comment: 26 pages, 1 figure; v2: typos corrected, topology arguments
corrected, discussion of black rings and dipole charge added, references
added, version to appear in Classical and Quantum Gravit